Focusing magnet

ABSTRACT

An electromagnet pole piece structure having four or more pole pieces with the surface of each piece being a modified hyperboloid in the vicinity of the central magnetic focusing gap to improve field linearity, reduce variations in effective length at various angles and radii and minimize field distortions resulting from fringe effects at entrance and exit.

United States Patent [191 Oster [111 3,831,121 Aug. 20, 1974 FOCUSING MAGNET [75] Inventor:

[73] Assignee: Magna Tek Systems, Inc., Hayward,

Calif.

[22] Filed: July 10, 1973 [21] Appl. No.: 378,013

[52] US. Cl. 335/210, 328/228 [51] Int. Cl. H0lf 7/00 [58] Field of Search 335/210, 209, 213, 296,

[56] References Cited UNITED STATES PATENTS 2,882,396 4/1959 Courant et a1. 328/256 X Eugene L. Oster, Sunnyvale, Calif.

3,197,678 7/1965 Primas 335/209 3,388,359 6/1968 Lambertson 335/210 3,393,385 7/1968 Danby et a1 335/210 Primary Examiner-George Harris Attorney, Agent, or Firm-Gregg, Hendricson & Caplan [57] ABSTRACT An electromagnet pole piece structure having four or more pole pieces with the surface of each piece being a modified hyperboloid in the vicinity of the central magnetic focusing gap to improve field linearity, reduce variations in effective length at various angles and radii and minimize field distortions resulting from fringe effects at entrance and exit.

5 Claims, 14 Drawing Figures BACKGROUND OF INVENTION It has long been known that charged particles such as electrons are affected by magnetic fields and the principle of strong focusing enunciated in US Pat. No. 2,736,799 issued to Nicholas Christofilos provided a way of focusing an electron beam, for example by magnetic fields. This principle has been widely employed and a variety of focusing magnets structures have been developed for use with particle accelerators and transport systems therefor. One conventional magnet structure comprises a quadrupole with four pole pieces disposed in quadrature and generally having curved facing surfaces to define an aperture through which a charged particle beam is passed for magnetic focusing.

Following relatively early developments of strong focusing magnet structures, the state of the art has remained relatively unchanged for some period of time, at least as regards medium and lower energy accelerator transport systems. Conventional quadrupole designs for a strong focusing of charged particle beams, for example, have the disadvantage of establishing nonlinear field gradients in the magnet aperture and also differing field gradients in different directions transverse to a beam axis. Such structures also suffer from the defect of varying effective magnet lengths at various angles and radii in the aperture plane.

It is also recognized that conventional magnet structures embody undesirable fringe effects resulting in field distortions on opposite sides of the main focusing volume. The foregoing results in a useful diameter for strong focusing of only about 60 to 65 percent of the full field aperture diameter which is then only about 36 to .42 percent of the full aperture cross sectional area. Inasmuch as very precise magnetic field relationships are often required for strong focusing, the useful focusing area may be considered as that portion of the magnetic field area having no more than k to 1 percent field variation from a true quadrupole field. It is also noted that undesirable end effects and fringe effects require added magnet length so that length to aperture ratios of less than 2:1 are almost never employed.

SUMMARY OF INVENTION The present invention provides an improved quadrupole magnet pole structure in which the pole configuration is a surface of revolution such as a hyperboloid which becomes flatter as the aperture increases. A preferred embodiment of the invention has a configuration providing a slowly increasing air gap or aperture with a constantly changing correction such that X Y=Ka /2, wherein Y and X are the ordinate and abscissa, respectively, of a co-ordinate system centered at the center of the air gap or aperture with the pole piece oriented at 45 to the system and'a is the radius of the air gap to the innermost point of the pole pieces. The constant K in the foregoing relationship provides for slight deviations as may be required for different applications and conditions. This condition is maintained at least until the air gap or aperture and therefor the field-length product in the area becomes small as compared to the rest of the magnet. The foregoing condition is obtained by the provision of magnet pole pieces having a surface of revolution such as a hyperboloid configuration.

LII

DESCRIPTION OF FIGURES The present invention is illustrated as to a preferred embodiment thereof in the accompanying drawings wherein:

FIG. 1 is a schematic illustration of quadrupole magnet pole pieces in a central plane normal to a center line through the magnet aperture and containing certain notations helpful in defining relationships in the description of the present invention;

FIG. 2 is a graph of magnetic field versus magnet aperture radius for conventional quadrupole magnet pole pieces;

FIG. 3 is a schematic end elevational view of the four magnet pole pieces formed in accordance with the present invention;

FIG. 4 is a partial longitudinal sectional view of a quadrupole magnet in accordance with the present invention and taken in the plane 4-4 of FIG. 3;

FIG. 5 is a schematic plan view of a single pole piece of a magnet in accordance with the present invention and FIGS. 5A to SF are schematic sectional views taken in the planes A-A to F-F of FIG. 5 and illustrating pole piece curvatures at successive planes displaced from the center of the pole piece;

FIG. 6 is a front elevational view of a focusing magnet in accordance with the present invention;

FIG. 7 is a graph of quadrupole magnet field strength versus ideal for a quadrupole magnet of the present invention at curve A and a conventional quadrupole magnet at curve B; and

FIG. 8 is a graph in polar co-ordinates illustrating the aperture area of a 0.1 percent variation of field strength from ideal field strength of a quadrupole magnet for a magnet of the present invention as shown at curve A and conventional quadrupole magnets as shown at curves B and C.

DESCRIPTION OF PREFERRED EMBODIMENT A preferred embodiment of the present invention as described herein is a quadrupole magnet; however, the invention is equally applicable to other magnets such as six pole and eight pole magnets.

Before considering the details of the present invention it is noted that a quadrupole magnet is conventionally comprised as a structure having four orthogonally disposed magnet poles with the pole tips spaced apart to define a magnet aperture. Magnet coils are wound about the pole pieces which have the bases thereof connected together as by an iron ring or the like to provide a flux path. In discussing quadrupole magnets it is convenient to employ certain conventions and certain of these are illustrated in FIG. 1 of the drawings. Magnet pole pieces 11, 12, 13 and 14 are illustrated with respect to a rectangular co-ordinate system in X and Y lying in a plane normal to and transverse of a Z axis extending through a magnet aperture defined by the pole pieces. The total magnet aperture is normally taken as a circle having a radius a extending from the Z axis to the closest point of the pole tips. Angular measurements are normally considered as being taken from the X axis and are designated B with the pole piece 12, for example, being oriented at B= 45. Aperture radius is designated r with pole piece width in the plane X-Y being' denominated d. Conventionally pole tips in a quadrupole magnet are formed with a curvature R in the X-Y or aperture plane.

It is desired, particularly for strong focusing, that a quadrupole magnet should have a field strength B which varies linearly with radius r in the magnet aperture. In FIG. 2 there is illustrated a plot of B versus r for an ideal quadrupole. In FIG. 2 there is also illustrated variations in the B versus r relation for conventional quadrupoles at B zero and B 45. It will be seen that the field strength versus radius varies from ideal in accordance with the direction chosen from the Z axis and for many applications this variation is at least disadvantageous, if not intolerable. Again taking the example of strong focusing, it is necessary that the magnet field strength be precisely the same about the circumference of each radius in the magnet aperture and it is common to consider the useful aperture as being the area in the )(Y plane having a maximum variation of field strength from ideal field strength of less than 0.01 percent to 0.05 percent.

A further problem in the field of quadrupole magnets employed, for example, in strong focusing, is the fringing effects of the magnetic field on opposite sides of a central X-Y plane.

Referring now to FIGS. 3 and 4, there will be seen to be schematically illustrated the improved quadrupole magnet in accordance with the present invention and particularly with regard to the pole tips thereof. Pole tips 21, 22, 23 and 24 are mounted in quadrature and each is formed with identical curvatures, as further described below. In FIG. 4 there are schematically illustrated magnet coils 26 and 27 about the pole pieces 21 and 23 for inducing a magnetic flux therein. There is also illustrated in FIG. 4 end plates 31 and 32 having central apertures 33 and 34, respectively, and disposed on opposite sides of the magnet pole pieces. These end plates may or may not be employed depending upon the application of the magnet. The general composition of the quadrupole magnet of the present invention is conventional; however, the present invention provides a particular pole tip configuration for a quadrupole magnet significantly differing from prior art magnets to produce the advantageous results of the present invention.

Referring now to FIG. and FIGS. 5A to SF, there will be seen to be schematically illustrated a single pole piece 22, for example, having the configuration of the present invention. In FIGS. 5A to SF there are illustrated the curvatures of the pole piece at successive parallel planes based outwardly from the center of the pole piece. It is not attempted in these Figures to precisely identify the curvature other than to generally indicate the pole piece configuration. In accordance with the present invention each of the pole pieces shall have the configuration of a surface of revolution and preferably that of a hyperboloid. Employing the conventions identified above in connection with FIG. 1, the pole piece curvature is defined as X Y Ka /2. This is the equation of a hyperboloid with a small correction K and will be seen to provide curvature in all directions. It will, of course, be appreciated that only the pole tip is formed with this curvature. The remainder of the pole piece has sides upon which a coil may be wound or disposed for inducing the flux in the magnet. These sides may be straight for medium power magnets, stepped for low power magnets or tapered for high power magnets. The pole pieces of this invention preferably have a substantially hyperboloid configuration and the constant K provides for slight variations from a true hyperboloid.

In FIGS. 7 and 8 there are illustrated field measurements taken with a quadrupole magnet of the present invention as compared to a conventional quadrupole magnet. Curve B of FIG. 7 shows the variation in field strength compared to theoretically proper field strength for a quadrupole magnet of conventional design and it will be seen that a substantially zero variation exists only over about half of the aperture radius. The curve B is seen to depart rather radically from ideal at increasing radius. Curve A, representing a quadrupole magnet having the pole piece configuration of the present invention on the other hand, has a substantially zero field gradient variation from ideal over about three-quarters of the radius of the aperture and has AB/B about 0.01 for the complete aperture. This will be seen to be a very marked improvement over the prior art and is particularly important in focusing magnets for electron beams and the like.

FIG. 8 illustrates at Curves B and C field strength variations for two conventional quadrupole magnets while Curve A represents the area of 0.1 percent variation of field strength over ideal strength for a quadrupole magnet of the present invention. Assuming, for example, as stated above, that the useful aperture is limited to 0.1 AB/B for a charged particle beam focusing magnet, it will then be noted from FIG. 8 that the present magnet provides for utilization of an entire magnet aperture while conventional magnets are severely limited in this respect.

It is also noted that the present invention provides a marked decrease in length-to-aperture ratio. Conventionally it is necessary to employ a substantial magnet length along the Z axis and in practice length-toaperture ratios of 2:1 areabout the minimum useable. The present invention, on the other hand, provides for a pole length-to-aperture ratio of almost 1:1 to thereby reduce the size and cost of a magnet formed in accordance with the present invention.

Although the present invention has been described with respect to a quadrupole magnet, it may also be employed with magnets having a larger number of poles. For a six pole magnet a 60 hyperboloid is employed and for an eight pole magnet a 45 hyperboloid is employed. It will be apparent to those skilled in the art that modifications and variations of the invention are possible and thus it is not intended to limit the invention to the precise terms of description nor details of illustration.

What is claimed is:

l. A multiple pole magnet structure comprising a plurality of aneven number greater than two of magnet poles having magnet coils coupled thereto and having pole tips substantially equally spaced apart about a magnet aperture,

said pole tips each having a surface of revolution configuration facing an opposite pole tip with the axis of revolution being coincident.

2. The magnet structure of claim 1 further defined by said pole tips having a substantially hyperboloid configuration.

3. The magnet structure of claim 1 further defined by said pole tips being spaced from a central axis normal to an aperture plane having co-ordinate XY axes in such plane and the curvature of each of said pole tips being defined by the relationship X Y Ka /2 where a 6 is the radial distance from said central axis to the pole said pole tips having a substantially hyperboloid surtip and K is a correction constant of small value providface of revolution configuration. ing minor deviation from a true hyperboloid configura- 5. The magnet structure of claim 4 further defined by tion. the surface of each of said pole tips being spaced from 4. A quadrupole magnet structure comprising 5 a central axis normal to an aperture plane in a cofour orthogonally disposed magnet poles having magordinate XY axis in such plane and parallel planes by net coils coupled thereto and having the pole tips substantially XY =a /2 where a is the radial distance thereof spaced apart to define a magnet aperture, from the central axis to the closest point on the pole tip. 

1. A multiple pole magnet structure comprising a plurality of an even number greater than two of magnet poles having magnet coils coupled thereto and having pole tips substantially equally spaced apart about a magnet aperture, said pole tips each having a surface of revolution configuration facing an opposite pole tip with the axis of revolution being coincident.
 2. The magnet structure of claim 1 further defined by said pole tips having a substantially hyperboloid configuration.
 3. The magnet structure of claim 1 further defined by said pole tips being spaced from a central axis normal to an aperture plane having co-ordinate XY axes in such plane and the curvature of each of said pole tips being defined by the relationship XY Ka2/2 where a is the radial distance from said central axis to the pole tip and K is a correction constant of small value providing minor deviation from a true hyperboloid configuration.
 4. A quadrupole magnet structure comprising four orthogonally disposed magnet poles having magnet coils coupled thereto and having the pole tips thereof spaced apart to define a magnet aperture, said pole tips having a substantially hyperboloid surface of revolution configuration.
 5. The magnet structure of claim 4 further defined by the surface of each of said pole tips being spaced from a central axis normal to an aperture plane in a co-ordinate XY axis in such plane and parallel planes by substantially XY a2/2 where a is the radial distance from the central axis to the closest point on the pole tip. 